Uniqueness of a solution of an ice plate oscillation problem in a channel

In this paper an initial-boundary value problem for two mathematical models of elastic and viscoelastic oscillations of a thin ice plate in an infinite channel under the action of external load is considered in terms of the linear theory of hydroelasticity. The viscosity of ice is treated in the context of the Kelvin–Voigt model. The joint system of equations for the ice plate and an ideal fluid is considered. Boundary conditions are conditions of clamped edges for the ice plate at the walls of the channel, condition of impermeability for the flow velocity potential and the damping conditions for the oscillations at infinity. The uniqueness theorem for the classical solution of the initial-boundary value problem is proved.